Seeing sequences

Abstract
This article discusses Charles Parsons’ conception of mathematical intuition. Intuition, for Parsons, involves seeing-as: in seeing the sequences I I I and I I I as the same type, one intuits the type. The type is abstract, but intuiting the type is supposed to be epistemically analogous to ordinary perception of physical objects. And some non-trivial mathematical knowledge is supposed to be intuitable in this way, again in a way analogous to ordinary perceptual knowledge. In particular, the successor axioms are supposed to be knowable intuitively.This conception has the resources to respond to some familiar objections to mathematical intuition. But the analogy to ordinary perception is weaker than it looks, and the warrant provided for non-trivial mathematical beliefs by intuition of this sort is weak too weak, perhaps, to yield any mathematical knowledge
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